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Statistical Probabilities and Distributions

3 Level Study Guide -- Central Limit Theorem

Directions Check the statements which you believe say what the author says.
Sometimes, the exact words are used; at other times, other words may be used.

  1. Ensuring random sampling, free of sampling errors, is important.
  2. The Central Limit Theorem helps us approximate the center location and width of any distribution.
  3. The empirical rule states that about 95% of a normally distributed population is within 2 standard deviations of the mean.
  4. The margin of error is the product of the standard error of the mean and a carefully chosen z-score.
  5. Although a 95% confidence level is commonplace, life or death situations may require a higher confidence level.
  6. If your sample size is more than 5% of the population you should adjust the standard error upward by a certain factor.
Directions Check the statements which you feel represent the author's intended meaning.

  1. Time spent designing an experiment is time well spent.
  2. With large sample sizes, the mean of your sample means is less likely to be close to the true (population) mean.
  3. For samples with sizes of more than 30, the distribution of sample means can be well approximated by a normal distribution.
  4. If the empirical rule says 99.7% of a population is within three standard deviations of the mean, then a z-score of about 3 would produce a margin of error of about 99.7%.
  5. Both socialogists and medical researchers use a 95% confidence interval.
  6. If we replace the object before resampling, we can assume our population to be infinite.
Directions: Check the statements you agree with, and be ready to support your
choices with ideas from the text as well as your own knowledge and beliefs.

  1. You should have your experimental design checked by a statistician before collecting data.
  2. It is important for researchers to be able to generalize their results.
  3. Selecting a sample size is not important to the experimental design process.
  4. Speaking in terms of a margin of error is just another way of saying "We don't know for sure."
  5. A 95% confidence interval is quite acceptable for something as benign as the outcome of the presidential election in Ohio in Nov. 2004.
  6. The Hypergeometric distribution and the Finite Population Correction Factor are related at a deep mathematical level.
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